It's really your choice so please don't take this as advice, just my observations.
Whether you are working or not shouldn't affect your need for private health insurance unless u are earning enough that you want to avoid paying the Medicare levy surcharge.
Like you I think overall our public health system does a great job.
From what I have seen the main benefit of having private health insurance is that it will get you in sooner for elective surgery. However, the insurance by no means covers all costs, and there are likely to be gaps to pay. In a public hospital there are few extra costs, only really medication for discharge.
Extras cover may be worth it if you see a lot of complementary health professionals or need prescription glasses every couple of years. I figure it is cheaper to just pay full price to go to the dentist once a year and not be tied into ongoing monthly payments.